In this thesis, a recently developed particle-based method called multiparticle collision dynamics (MPC) is used to simulate steady flows through three-dimensional constricted axisymmetric cylinders. The work is motivated by complex particle interactions in blood flow such as aggregation and the need to be able to capture these effects in physiologically relevant complex flow geometries. This is the first time that MPC dynamics has been applied to simulate flows though constrictions. The particle collisions in MPC dynamics are numerically more efficient than other particle-based simulation methods. Particle interactions with the cylinder walls are modeled using bounce-back (BB) and loss in tangential, reversal of normal (LIT) boundary conditions. BB is an analog of the macroscopic no-slip boundary condition, and LIT gives slip. Finally, an averaging procedure is employed to make a connection with the solution to the Navier-Stokes equations. Interesting differences have been found in the velocity profiles obtained using MPC with BB and LIT, compared to Navier-Stokes.